Give the exact value of the trigonometric function:
arctan(√3)
or
tan ß = √3/1
You should recognize the 1:√3:2 right-angled triangle with angles 30º,60º,90º
we know that tan 60º = √3/1
so arctan√3 = 60º or pi/3 radians
To find the exact value of arctan(√3), we need to recall the special triangles and their angle measures.
In a 30-60-90 triangle, the sides are in the ratio of 1:√3:2, and the angles are 30°, 60°, and 90°.
By observing the ratio of the sides, we know that the tangent of the 30° angle is √3/1, or simply √3.
Since arctan is the inverse function of tangent, we can conclude that arctan(√3) is equal to 30°.
Therefore, the exact value of arctan(√3) is 30°.